Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-x5fd4 Total loading time: 0.459 Render date: 2021-02-26T05:23:04.671Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition

Published online by Cambridge University Press:  26 July 2019

Wenjie Zheng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
Shanxin Ruan
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
Yue Yang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China CAPT and BIC-ESAT, Peking University, Beijing 100871, China
Lin He
Affiliation:
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China CAPT and BIC-ESAT, Peking University, Beijing 100871, China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology of China, Shenzhen 518055, China
Corresponding
E-mail address:

Abstract

We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition. The images are extracted from a passive scalar field by a sliding window filter on the streamwise and wall-normal plane. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angle of spatially evolving filtered component fields at different scales ranging from a boundary-layer thickness to several viscous length scales. In general, the averaged inclination angles increase along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. Inspired by the coincidence of the increasing averaged inclination angle and the rise of the skin-friction coefficient, we propose a simple image-based model of the skin-friction coefficient. The model blends empirical formulae of the skin-friction coefficient in laminar and fully developed turbulent regions using the normalized averaged inclination angle of scalar structures at intermediate and small scales. The model prediction calculated from scalar images is validated by the results from the direct numerical simulation at two Mach numbers, 2.25 and 6, and the relative error can be less than 15 %.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.

References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Anderson, J. D. 2010 Fundamentals of Aerodynamics, 4th edn. McGraw-Hill.Google Scholar
Candes, E., Demanet, L., Donoho, D. & Ying, L. 2006 Fast discrete curvelet transforms. Multiscale Model. Simul. 5, 861899.CrossRefGoogle Scholar
Dhawan, S. & Narasimha, R. 1958 Some properties of boundary layer flow during the transition from laminar to turbulent motion. J. Fluid Mech. 3, 418436.CrossRefGoogle Scholar
van Driest, E. R.1952 Investigation of laminar boundary layer in compressible fluids using the Crocco method. NACA Tech. Note 2597.Google Scholar
van Driest, E. R. 1956 The problem of aerodynamic heating. Aeronaut. Engng Rev. 15, 2641.Google Scholar
Duan, L., Beekman, I. & Martin, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419445.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245267.CrossRefGoogle Scholar
Ducros, F., Comte, P. & Lesieur, M. 1996 Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 326, 136.Google Scholar
Duraisamy, K., Iaccarino, G. & Xiao, H. 2019 Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51, 357377.CrossRefGoogle Scholar
Durbin, P. A. 2018 Some recent developments in turbulence closure modeling. Annu. Rev. Fluid Mech. 50, 77103.CrossRefGoogle Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in a boundary layer – Part I. J. Aero. Sci. 18, 490498.Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, S124.CrossRefGoogle Scholar
Franko, K. J. & Lele, S. K. 2013 Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers. J. Fluid Mech. 730, 491532.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L7376.CrossRefGoogle Scholar
Gao, H., Fu, D.-X., Ma, Y.-W. & Li, X.-L. 2005 Direct numerical simulation of supersonic turbulent boundary layer flow. Chin. Phys. Lett. 22, 17091712.Google Scholar
Gomez, T., Flutet, V. & Sagaut, P. 2009 Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Phys. Rev. E 79, 035301.Google ScholarPubMed
Goyne, C. P., Stalker, R. J. & Paull, A. 2003 Skin-friction measurements in high-enthalpy hypersonic boundary layers. J. Fluid Mech. 485, 132.CrossRefGoogle Scholar
Hakkinen, R. J. 2004 Reflections on fifty years of skin friction measurement. In Proceedings of the 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference. AIAA.Google Scholar
He, L., Yi, S., Zhao, Y., Tian, L. & Chen, Z. 2011a Experimental study of a supersonic turbulent boundary layer using PIV. Sci. China Phys. Mech. Astron. 54, 17021709.CrossRefGoogle Scholar
He, L., Yi, S., Zhao, Y., Tian, L. & Chen, Z. 2011b Visualization of coherent structures in a supersonic flat-plate boundary layer. Chinese Sci. Bull. 56, 489494.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.CrossRefGoogle Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245283.CrossRefGoogle Scholar
Holden, M. S.1972 An experimental investigation of turbulent boundary layers at high Mach number and Reynolds numbers. NASA Tech. Rep. CR–112147.Google Scholar
Hutchins, N. & Choi, K.-S. 2002 Accurate measurements of local skin friction coefficient using hot-wire anemometry. Prog. Aerosp. Sci. 38, 421446.CrossRefGoogle Scholar
Jiang, G.-S. & Shu, C.-W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202228.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.CrossRefGoogle Scholar
Lee, C. B. & Wu, J. Z. 2008 Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802.Google Scholar
Li, X., Fu, D. & Ma, Y. 2010 Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack. Phys. Fluids 22, 025105.CrossRefGoogle Scholar
Marusic, I. & Monty, J. P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 4974.CrossRefGoogle Scholar
Menter, F. R., Langtry, R. & Völker, S. 2006 Transition modelling for general purpose CFD codes. Flow Turbul. Combust. 77, 277303.CrossRefGoogle Scholar
Mishra, M., Liu, X., Skote, M. & Fu, C. W. 2014 Kolmogorov spectrum consistent optimization for multi-scale flow decomposition. Phys. Fluids 26, 055106.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2. 25. Phys. Fluids 16, 530.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.CrossRefGoogle Scholar
Rodriguez-Lopez, E., Bruce, P. J. K. & Buxton, O. R. H. 2015 A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile. Exp. Fluids 56, 68.CrossRefGoogle Scholar
Sayadi, T., Schmid, P. J., Nichols, J. W. & Moin, P. 2014 Reduced-order representation of near-wall structures in the late transitional boundary layer. J. Fluid Mech. 748, 278301.CrossRefGoogle Scholar
Schetz, J. A. 2010 Direct measurement of skin friction in complex flows. In Proceedings of the 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA.Google Scholar
Smith, M. W. & Smits, A. J. 1995 Visualization of the structure of supersonic turbulent boundary layers. Exp. Fluids 18, 288302.CrossRefGoogle Scholar
Spalding, D. B. & Chi, S. W. 1964 The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer. J. Fluid Mech. 18, 117143.CrossRefGoogle Scholar
Spina, E. F., Donovan, J. F. & Smits, A. J. 1991 On the structure of high-Reynolds-number supersonic turbulent boundary layers. J. Fluid Mech. 222, 293327.CrossRefGoogle Scholar
Suzen, Y. B. & Huang, P. G. 2000 Modeling of flow transition using an intermittency transport equation. Trans. ASME J. Fluids Engng 122, 273284.CrossRefGoogle Scholar
Tay, C. M. J., Khoo, B. C. & Chew, Y. T. 2012 Determination of hot-wire position from a solid wall in an opaque channel. Meas. Sci. Technol. 23, 085305.CrossRefGoogle Scholar
Tian, L., Yi, S., Zhao, Y., He, L. & Cheng, Z. 2009 Study of density field measurement based on NPLS technique in supersonic flow. Sci. China Ser. G-Phys. Mech. Astron. 52, 13571363.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Walters, D. K. & Cokljat, D. 2008 A three-equation eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow. Trans. ASME J. Fluids Engng 130, 121401.Google Scholar
Wang, L. & Fu, S. 2009 Modelling flow transition in a hypersonic boundary layer with Reynolds-averaged Navier–Stokes approach. Sci. China Ser. G-Phys. Mech. Astron. 52, 768774.CrossRefGoogle Scholar
Wang, L. & Lu, X.-Y. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255278.CrossRefGoogle Scholar
Wang, Q.-C., Wang, Z.-G., Sun, M.-B., Yang, R., Zhao, Y.-X. & Hu, Z. 2019 The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties. J. Fluid Mech. 863, 454493.CrossRefGoogle Scholar
Wang, Q.-C., Wang, Z.-G. & Zhao, Y.-X. 2016 Structural responses of the supersonic turbulent boundary layer to expansions. Appl. Phys. Lett. 109, 124104.Google Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
White, F. M. & Christoph, G. H. 1972 A simple theory for the two-dimensional compressible turbulent boundary layer. Trans. ASME J. Basic Engng 94, 636642.CrossRefGoogle Scholar
Yang, Y. & Pullin, D. I. 2010 On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions. J. Fluid Mech. 661, 446481.CrossRefGoogle Scholar
Yang, Y. & Pullin, D. I. 2011 Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 6792.CrossRefGoogle Scholar
Yang, Y., Pullin, D. I. & Bermejo-Moreno, I. 2010 Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence. J. Fluid Mech. 654, 233270.CrossRefGoogle Scholar
Zhang, C., Duan, L. & Choudhari, M. M. 2017 Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6. J. Fluid Mech. 822, 530.CrossRefGoogle Scholar
Zhang, Y.-S., Bi, W.-T., Hussain, F. & She, Z.-S. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392420.CrossRefGoogle Scholar
Zhao, Y., Xia, Z., Shi, Y., Xiao, Z. & Chen, S. 2014 Constrained large-eddy simulation of laminar-turbulent transition in channel flow. Phys. Fluids 26, 095103.CrossRefGoogle Scholar
Zhao, Y., Xiong, S., Yang, Y. & Chen, S. 2018 Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Phys. Rev. Fluids 3, 074701.CrossRefGoogle Scholar
Zhao, Y., Yang, Y. & Chen, S. 2016 Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech. 793, 840876.CrossRefGoogle Scholar
Zheng, W., Yang, Y. & Chen, S. 2016 Evolutionary geometry of Lagrangian structures in a transitional boundary layer. Phys. Fluids 28, 035110.CrossRefGoogle Scholar
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid Mech. 44, 527561.CrossRefGoogle Scholar
Zhu, Y., Yuan, H., Zhang, C. & Lee, C. 2013 Image-preprocessing method for near-wall particle image velocimetry (PIV) image interrogation with very large in-plane displacement. Meas. Sci. Technol. 24, 125302.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 18
Total number of PDF views: 274 *
View data table for this chart

* Views captured on Cambridge Core between 26th July 2019 - 26th February 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *